Aircraft: SMALL TRANSPORT; LOW WING; 2 TURBOJET ENG
Phase of flight: Final Approach
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance

I was working ground control and a runway change was initiated to runway 11 and 5. Previously we were on Runway 29 and 23 for the shift I was working. Maybe ten minutes after the runway change was initiated and I made the ATIS broadcasting the appropriate ATIS; I taxied Aircraft Y to runway 29 (the previous runway in use) marked the strip for runway 29 and switched the pilot to the tower. I then was made aware of the situation when the local controller began giving traffic alerts to Aircraft Y and Aircraft X on final for runway 11. Aircraft Y departed opposite direction into Aircraft X and became a direct conflict.I believe a visual reminder of what runways are in use immediately after a runway change on the console would serve as a memory jogger. Muscle memory of repeating the same actions all day over and over again; only to change to the complete opposite can cause confusion and I believe a runway in use sign would help. Ground Control (GC) taxied Aircraft Y to runway 29. The active runway was 11. The runways had been switched and this was the first aircraft to depart the airport. Aircraft X was vectored for the ILS 11. I had stood up to look at the lighting panel and Aircraft Y calls ready for takeoff runway 29. I was using a hand set because I had left my headset in the tracon. I missed Aircraft Y saying he was at runway 29. Aircraft X calls after Aircraft Y and is on final runway 11. I clear Aircraft X to land Runway 11. I go straight to Aircraft Y and clear them for takeoff Runway 11 Heading 050. Aircraft Y questions the Heading and I said 'Affirmative heading 050 for Aircraft Y.' I told Aircraft Y of the traffic on 7 mile final runway 11. I scanned the runway and saw flashing lights at the approach end of runway 11 and did the scan of the rest of the runway. I did not see the aircraft at the approach end of runway 29. The flashing lights I saw where the barrier lights that separate A1 and A2. After clearing Aircraft Y for takeoff I looked up at the Dbrite to see where Aircraft X was and then I looked down to my notepad to write Aircraft X on the arrival column. I then went to the Aircraft Y strip to write the heading down and then looked back up to see where Aircraft Y was. Out of the corner of my eye I see flashing lights and it is Aircraft Y going the wrong way. I looked back at the strip and it had runway 29 on it. I looked back up at the Dbrite and see Aircraft X and I told Aircraft X to go around climb maintain 4000. I then go back to Aircraft Y and tell them to turn right heading 050 immediately. I go back to Aircraft X and issue a traffic alert and tell him to turn right heading 180 then to Aircraft Y I issued a traffic alert and the aircraft passed to the north and south.I had earlier in the day thought about going home sick because I was tired. I didn't for several reasons. We are at minimal staff; I was the late person; and I have been counseled on taking sick leave. The event happened because Aircraft Y was taxied to the wrong runway. The second problem happened when I missed the call saying Aircraft Y was at runway 29; possibly due to having the hand set and not the head set; the pilot did not question the clearance for takeoff on a different runway. Better communication; seeing the red flag when a pilot questions anything. Not using a Hand set. Don't send and aircraft to the wrong runway. A visual aid of some sort to indicate the runway in use would help when switching runways. It happens frequently; sending an aircraft to the wrong runway after a runway change. CAE Ground Controller taxis aircraft to Runway 29. Previously the airport was departing Runway 29; and ten minutes ago changed to using Runways 11 and 5. Ground Control later hears Local Control issuing traffic alerts to the aircraft he taxied to Runway 29 and another aircraft on final for Runway 11.